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Figure 1, Find the area of the Grayed triangle

Can you help me find the area of the gray triangle in the given figure. I'm having a hard time finding the base value of the triangle, I've managed to find the sides for the big triangle but not for the greyed area. Thanks in advance to those that will help.

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You need something that determines the location of $C$. Without that, you can't determine the area. – Daniel Fischer Jan 16 '14 at 16:38

As mentioned in the comments, there simply isn't enough information. All you know about the grayed triangle is that it is a right triangle with one of its legs having length $4,$ and the other having length somewhere between $0$ and $4\sqrt3.$ With only this information, the best we can conclude is that the grayed triangle can have any area between $0$ and $8\sqrt3.$ (And I do mean any such area. All we have to do is position $C$ appropriately.)

Is there perhaps some other information that you left out because you weren't sure how it was relevant, or because you missed it on your first read-through?

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Thank you for your comments, I also thought that yes it may be missing a value and I agree with both of the two comments above, but this is all there is. I guess that's why no one in class got the answer. Thank you for putting my mind at ease, I somehow knew that I can't work on the problem and looked back on ASA SAS and other postulates, I had to make sure that the problem is indeed unsolvable. Thanks again for putting me at ease, Kudos. – Tara Salvador Jan 16 '14 at 17:21

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